Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

A survey asked a random sample of 250 adults in Fromleigh to complete a questionnaire about their travel.
(a)[3]

The sample showed that 102 adults travel by bus. Find an approximate $90\%$ confidence interval for the proportion of all the adults in Fromleigh who travel by bus.

(b)[3]

The survey included a question about the amount, $x$ dollars, spent on travel per year. The results are summarised as follows: $n = 250$, $\sum x = 50460$, $\sum x^2 = 19\,854\,200$. Find unbiased estimates of the population mean and variance of the amount spent per year on travel.

(c)[1]

A councillor wanted to select a random sample of houses in Fromleigh. He planned to choose the first house on each of the 143 streets in Fromleigh. Explain why this would not give a random sample.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Valid variance expression for the sampling distribution of a proportion, $\dfrac{102}{250}\times\dfrac{250-102}{250\times250}$.

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